Question

an iron rod is length 50m when the temperature is 20 degree celcuis by how much will it expand when the temperature rises to 30 degree celcuis

Answer 1

By the definition of the linear thermal expansion we have:

$$\Delta L = \alpha L_0 \Delta T,$$

here, $\Delta L$ is the difference in the length of the iron rod after the change in the temperature (or the expansion of the rod) , $L_0 = 50 m$ is the original length of the iron rod, $\alpha = 11.8 \cdot 10^{-6} \dfrac{1}{^{\circ}C}$ is the coefficient of linear expansion for the iron rod and $\Delta T = T_{final} - T_{initial} = 30^{\circ}C - 20^{\circ}C = 10^{\circ}C$ is the change in temperature.

Then, from this formula we can calculate the linear expansion of the iron rod:

$$\Delta L = 11.8 \cdot 10^{-6} \dfrac{1}{^{\circ}C} \cdot 50 m \cdot 10^{\circ}C = 5.9 \cdot 10^{-3} m.$$

Answer:

$\Delta L = 5.9 \cdot 10^{-3} m.$